An algebraic flux correction scheme facilitating the use of Newton-like solution strategies

Building on recent advances in the analysis and design of algebraic flux correction (AFC) schemes, new differentiable limiter functions are constructed for efficient nonlinear solution strategies. The proposed scaling parameters used to limit artificial diffusion operators incorporated into residual a high order target scheme produce accurate bound-preserving finite element approximations hyperbolic problems. Due this stabilization procedure, occurring system becomes highly computation corresponding solutions is challenging task. presented regularization approach makes AFC twice continuously so that Newton’s method converges quadratically sufficiently good initial guesses. Furthermore, performance each iteration improved by expressing Jacobian as sum product matrices having same sparsity pattern Galerkin matrix. Eventually, methodology validated numerically applying it several numerical benchmarks.